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156
CUTE: Constrained and unconstrained testing environment
, 1993
"... The purpose of this paper is to discuss the scope and functionality of a versatile environment for testing small and largescale nonlinear optimization algorithms. Although many of these facilities were originally produced by the authors in conjunction with the software package LANCELOT, we belie ..."
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Cited by 188 (3 self)
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The purpose of this paper is to discuss the scope and functionality of a versatile environment for testing small and largescale nonlinear optimization algorithms. Although many of these facilities were originally produced by the authors in conjunction with the software package LANCELOT, we believe that they will be useful in their own right and should be available to researchers for their development of optimization software. The tools are available by anonymous ftp from a number of sources and may, in many cases, be installed automatically. The scope of a major collection of test problems written in the standard input format (SIF) used by the LANCELOT software package is described. Recognising that most software was not written with the SIF in mind, we provide tools to assist in building an interface between this input format and other optimization packages. These tools already provide a link between the SIF and an number of existing packages, including MINOS and OSL. In ad...
Solving LargeScale Linear Programs by InteriorPoint Methods Under the MATLAB Environment
 Optimization Methods and Software
, 1996
"... In this paper, we describe our implementation of a primaldual infeasibleinteriorpoint algorithm for largescale linear programming under the MATLAB 1 environment. The resulting software is called LIPSOL  Linearprogramming InteriorPoint SOLvers. LIPSOL is designed to take the advantages of M ..."
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Cited by 96 (1 self)
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In this paper, we describe our implementation of a primaldual infeasibleinteriorpoint algorithm for largescale linear programming under the MATLAB 1 environment. The resulting software is called LIPSOL  Linearprogramming InteriorPoint SOLvers. LIPSOL is designed to take the advantages of MATLAB's sparsematrix functions and external interface facilities, and of existing Fortran sparse Cholesky codes. Under the MATLAB environment, LIPSOL inherits a high degree of simplicity and versatility in comparison to its counterparts in Fortran or C language. More importantly, our extensive computational results demonstrate that LIPSOL also attains an impressive performance comparable with that of efficient Fortran or C codes in solving largescale problems. In addition, we discuss in detail a technique for overcoming numerical instability in Cholesky factorization at the endstage of iterations in interiorpoint algorithms. Keywords: Linear programming, PrimalDual infeasibleinteriorp...
A TwoDimensional Data Distribution Method For Parallel Sparse MatrixVector Multiplication
 SIAM REVIEW
"... A new method is presented for distributing data in sparse matrixvector multiplication. The method is twodimensional, tries to minimise the true communication volume, and also tries to spread the computation and communication work evenly over the processors. The method starts with a recursive bipar ..."
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Cited by 82 (9 self)
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A new method is presented for distributing data in sparse matrixvector multiplication. The method is twodimensional, tries to minimise the true communication volume, and also tries to spread the computation and communication work evenly over the processors. The method starts with a recursive bipartitioning of the sparse matrix, each time splitting a rectangular matrix into two parts with a nearly equal number of nonzeros. The communication volume caused by the split is minimised. After the matrix partitioning, the input and output vectors are partitioned with the objective of minimising the maximum communication volume per processor. Experimental results of our implementation, Mondriaan, for a set of sparse test matrices show a reduction in communication compared to onedimensional methods, and in general a good balance in the communication work.
Implementation of interior  point methods for large scale linear programs,
 In Interior Point Methods of Mathematical Programming,
, 1996
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An Implementation Of Karmarkar's Algorithm For Linear Programming
 Mathematical Programming
, 1986
"... . This paper describes the implementation of power series dual affine scaling variants of Karmarkar's algorithm for linear programming. Based on a continuous version of Karmarkar's algorithm, two variants resulting from first and second order approximations of the continuous trajectory are ..."
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Cited by 76 (4 self)
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. This paper describes the implementation of power series dual affine scaling variants of Karmarkar's algorithm for linear programming. Based on a continuous version of Karmarkar's algorithm, two variants resulting from first and second order approximations of the continuous trajectory are implemented and tested. Linear programs are expressed in an inequality form, which allows for the inexact computation of the algorithm's direction of improvement, resulting in a significant computational advantage. Implementation issues particular to this family of algorithms, such as treatment of dense columns, are discussed. The code is tested on several standard linear programming problems and compares favorably with the simplex code MINOS 4.0. 1. INTRODUCTION We describe in this paper a family of interior point power series affine scaling algorithms based on the linear programming algorithm presented by Karmarkar (1984). Two algorithms from this family, corresponding to first and second order pow...
Symmetric quasidefinite matrices
 SIAM Journal on Optimization
, 1995
"... We say that a symmetric matrix K is quasidefinite if it has the form ..."
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Cited by 72 (4 self)
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We say that a symmetric matrix K is quasidefinite if it has the form
Multiple centrality corrections in a primaldual method for linear programming,
 Computational Optimization and Applications
, 1996
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Permuting Sparse Rectangular Matrices into BlockDiagonal Form
 SIAM Journal on Scientific Computing
, 2002
"... We investigate the problem of permuting a sparse rectangular matrix into block diagonal form. Block diagonal form of a matrix grants an inherent parallelism for solving the deriving problem, as recently investigated in the context of mathematical programming, LU factorization and QR factorization. W ..."
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Cited by 56 (18 self)
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We investigate the problem of permuting a sparse rectangular matrix into block diagonal form. Block diagonal form of a matrix grants an inherent parallelism for solving the deriving problem, as recently investigated in the context of mathematical programming, LU factorization and QR factorization. We propose bipartite graph and hypergraph models to represent the nonzero structure of a matrix, which reduce the permutation problem to those of graph partitioning by vertex separator and hypergraph partitioning, respectively. Our experiments on a wide range of matrices, using stateoftheart graph and hypergraph partitioning tools MeTiS and PaToH, revealed that the proposed methods yield very effective solutions both in terms of solution quality and runtime.